The present invention relates to a method and apparatus for identification of effective elements in complex systems, and, more particularly, but not exclusively to a method and apparatus that samples the activity of the complex system under selective silencing of elements and analyzes the results.
The “effective elements” approach to complex systems has its roots in computational neuroscience, and is derived from the research of the present inventors into the analysis of localization of function in neural networks. The classical problem of localization of function essentially translates to trying to answer the question, “which system elements contribute to a given task performed by a network/agent/animal?”. The problem is a very difficult one, in neuroscience as well as in genetic and metabolic networks studied in functional genomics, since the network investigated may be capable of performing multiple and unrelated tasks, often in parallel, and individual elements may have functions that interrelate with other elements etc. Each task recruits some of the elements of the system, and often the same element participates in several tasks. This poses a very serious challenge when one attempts to identify the roles of the network elements, and to assess their contributions to the different tasks.
In neuroscience research there have traditionally been two main conceptual approaches aimed at addressing the central question of function localization. The first is termed the Correlational approach; employing various analysis methods it correlates between measurements such as electrical recordings of neural activity or functional imaging intensities on the one hand and other indices of network/agent performance on the other. With the correlational approach, it is difficult to correctly identify the “core set” of elements that contribute exclusively to the task in hand and hence are those responsible for it. This is because additional elements that are not really in the core set may be activated by core set elements and show high correlations with the task measured, even though they are in fact making no contribution whatsoever, and hence may be falsely included in the core set by such a correlational method. To overcome these inherent shortcomings, another parallel approach has been traditionally taken in neuroscience. This approach, known as the lesioning or silencing approach, has its roots in classical systems analysis theory, where the structure and dynamics of a system are studied by inducing lesions that perturb the system from its normal functioning state and then track its corresponding behavior. In contradistinction to the correlational approach, Lesioning in principle enables one to correctly identify the system elements that are really responsible for a given task, and to precisely quantify their respective contributions.
Because of the significant difficulties involved in conducting lesioning experiments in animals, the large majority of these studies have employed single lesions, where only one element of the system is ablated at any given time. Such single lesions (or, their conceptually equivalent “single knockout” experiments in functional genomics) are very limited in their ability to reveal the significance of elements which interact in complex ways in network processing. For example, when two elements have a high degree of redundancy with respect to the processing of a function to which they equally contribute, lesioning either element alone will not reveal its true significance, since no reduction in function performance will occur. Each time the function of the lesioned element will be fulfilled by the other element and the two elements will appear to be ineffective even though this is far from the truth.
The problematic and limited value of single lesion analysis has already been widely noted in neuroscience literature. Another classic example is the paradoxical lesioning effect, where lesioning area A alone is harmful but lesioning area A given that area B is lesioned is beneficial, hence the apparent “paradox”. Importantly, it demonstrates that looking at a single lesion alone may be misleading, as the beneficial influence of an area depends on the general state of the system.
Given these inherent limitations of the single lesioning approach, it became clear to us more than two years ago that if one wants to obtain a precise description of how a given function is localized in a network performing that function, then two basic things should be done: First, one has to perform multi-lesioning (or, in functional genomics, multi-silencing) perturbation experiments to the system examined. In each such experiment, a set of elements is lesioned concurrently, and the resulting performance of the network is recorded. Second, after gathering a data set composed of many such multi-lesioning experiments and their corresponding performance measurements, one needs to find a method of analysis capable of using the data from numerous multi-lesioning experiments, and computing the contributions of each of the elements to the function (task) studied. The analysis should be capable of taking into account that some, if not many of the elements in the system may make vanishingly small contributions to any given task.
In previous work, the present inventors developed a novel Functional Contribution Analysis (FCA). The FCA multi-lesioning framework gives a rigorous, operative definition for the neurons' contributions to the system's performance in various tasks, and an algorithm for multi-lesion analysis to measure them by minimizing the performance prediction error over unseen test lesions data. The FCA was developed and studied in the theoretical modeling framework of neurally-driven evolved autonomous agents (EAAs).
The FCA enabled initial multi-lesion analysis of some simple small neurocontroller neural networks that had emerged in EAA networks. However, it was not sufficiently accurate and powerful for the analysis of biological “paradoxical” lesioning data of auditory processing in cats, see hereinbelow. Moreover, the conceptual core of the FCA is an operational definition, attempting to minimize the performance prediction error of the algorithm on new, unseen lesions. As such, there is no inherent notion of correctness of the solutions found, and the uniqueness of the solution is not guaranteed. Thus direct use of the FCA does not in fact characterize the contributions of individual elements.
There is thus a widely recognized need for, and it would be highly advantageous to have, a system for the analysis of the effectiveness of elements in a complex system which is devoid of the above limitations and in particular does provide a unique solution for a given input.